University Of Tehran Press Journal of Algorithms and Computation 2476-2776 52 2 2020 12 01 On Hardy's Apology Numbers 67 83 79248 10.22059/jac.2020.79248 EN Dr. Henk Koppelaar Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The NetherlandsVredenburchstede 20 Peyman Nasehpour Department of Engineering Science \\ Golpayegan University of Technology Journal Article 2020 12 29 Twelve well known `Recreational' numbers are generalized and classified in three generalized types Hardy, Dudeney, and Wells. A novel proof method to limit the search for the numbers is exemplified for each of the types. Combinatorial operators are defined to ease programming the search. Hardy's apology numbers Armstrong numbers Dudeney numbers Wells numbers https://jac.ut.ac.ir/article_79248_56d3c030088a170a3906b627fcde5388.pdf